Definition Parallelogram is a trapezoid with 2 pairs of parallel sides
Properties Side Properties
1. Opposite sides are congruent
Angle Properties
1. Opposite angles are congruent Example Proof
Prove: Angle APE is congruent to Angle ARE
Angle PAR is congruent to Angle PER
2. Consecutive angles are supplementary Example Proof
Prove: Angle ARG and Angle ARE are supplementary
Diagonal Properties
1. Diagonals bisect each other Segment AE bisects Segment PR
Segment LA is congruent to Segment LE
Segment PR bisects Segment AE
Segment LP is congruent to Segment LR
2. *Oppositely oriented triangles formed by diagonals are congruent Example Proof
Prove: Triangle RAT is congruent to Triangle CAE
This property is the most important of a parallelogram for the following reasons:
- Knowing that opposite triangle pairs are congruent, the congruence of their corresponding sides and angles can be proved by CPCTC. Such information can help find side and angle measurements
Parallelogram is a trapezoid with 2 pairs of parallel sides
Properties
Side Properties
1. Opposite sides are congruent
Angle Properties
1. Opposite angles are congruent
Example Proof
Prove: Angle APE is congruent to Angle ARE
Angle PAR is congruent to Angle PER
2. Consecutive angles are supplementary
Example Proof
Prove: Angle ARG and Angle ARE are supplementary
Diagonal Properties
1. Diagonals bisect each other
Segment AE bisects Segment PR
Segment LA is congruent to Segment LE
Segment PR bisects Segment AE
Segment LP is congruent to Segment LR
2. *Oppositely oriented triangles formed by diagonals are congruent
Example Proof
Prove: Triangle RAT is congruent to Triangle CAE
This property is the most important of a parallelogram for the following reasons:
- Knowing that opposite triangle pairs are congruent, the congruence of their corresponding sides and angles can be proved by CPCTC. Such information can help find side and angle measurements